# Alternate solutions to Resistance of a Conical Frustum

Since for a cylinder $$R = \rho\frac{\text{length}}{\text{Area}}$$

I assumed an equation of radius of this frustum: $$\text{radius} = \frac{b-a}{\text{length}}x$$

and then integrated to get the answer $$\int_0^L dR = \int_0^L \rho\frac{dx}{\pi\left(a+\frac{b-a}{L}x\right)^2}$$ $$R = \rho\frac{L}{\pi ab}$$

Are there other ways to find the Resistance without assuming an equation of radius (although it is not that difficult to assume such an equation using details given in the problem)

• You are not assuming anything here. You are merely using a fact given in the question that radius varies linearly and wrote the equation for that. There are other more complicated ways of solving this using different infinitesimal elements and putting them in parallel combination. Your method is by far, the easiest. – sarat.kant May 11 '16 at 12:20

The radius of the cross-section varies linearly from $a$ to $b$